Nonstationary vibration of a rotating shaft with nonlinear spring characteristics during acceleration through a critical speed (A critical speed of a summed-and-differential harmonic oscillation)

1990 ◽  
Vol 1 (5) ◽  
pp. 341-358 ◽  
Author(s):  
Yukio Ishida ◽  
Toshio Yamamoto ◽  
Takashi Ikeda ◽  
Shin Murakami
Keyword(s):  
Critical Speed ◽  
Harmonic Oscillation ◽  
Rotating Shaft ◽  
Nonlinear Spring ◽  
Nonstationary Vibration

Forced Oscillations of Rotating Shaft With Nonlinear Spring Characteristics and Internal Damping: Subharmonic Oscillation of Order 1/3 and Entrainment

1999 ◽  
Author(s):  
Yukio Ishida ◽  
Shin Murakami
Keyword(s):  
Critical Region ◽  
Critical Speed ◽  
Forced Oscillations ◽  
Ball Bearings ◽  
Internal Damping ◽  
Rotating Shaft ◽  
Nonlinear Spring ◽  
Subharmonic Oscillation

Abstract An elastic rotating shaft supported by ball bearings may have nonlinear spring characteristics due to clearance and internal damping due to friction between the shaft and the bearings. In such a system, self-excited oscillations appear in the post critical region and nonlinear forced oscillations appear at various resonance points. In this paper, a phenomenon in the neighborhood of the critical speed of the subharmonic oscillation of order 1/3 of a forward whirling mode is discussed. It is clarified that, similar to the case of the subharmonic oscillation of order 1/2 of a forward whirling mode, an entrainment phenomenon appears due to the interplay between self-excited oscillations and forced oscillations.

Nonstationary Vibration of a Rotating Shaft With Nonlinear Spring Characteristics During Acceleration Through a Major Critical Speed: A Discussion by the Asymptotic Method and the FFT Method

1993 ◽  
Author(s):  
Yukio Ishida ◽  
Kimihiko Yasuda ◽  
Shin Murakami
Keyword(s):  
Asymptotic Method ◽  
Critical Speed ◽  
Approximate Solutions ◽  
Rotating Shaft ◽  
Amplitude Variation ◽  
Nonlinear Spring ◽  
First Order ◽  
First Approximation ◽  
Nonlinear Components ◽  
Nonstationary Oscillations

Abstract Nonstationary vibrations at the major critical speed of a rotating shaft with nonlinear spring characteristics are discussced. Firstly, the first order approximate solutions of steady-state and nonstationary oscillations are obtained by the asymptotic method. The relations between these approximate solutions and the nonlinear components in the polar coordinate expression are investigated. It is clarified that, similar to the case of the stationary oscillations, only the isotropic nonlinear component has influence on nonstationary oscillations in the first order approximation. Secondly, the complex-FFT method where non-stationary time histories obtained by numerical integrations of the equations of motion are treated as complex numbers in the complex plane which coincides with the whirling plane are proposed. By this method, the amplitude variation curves of each vibration component are obtained. From the comparison of the amplitude variation curves of the first approximation of the asymptotic method, the solution of the complex-FFT method, and direct numerical integration, it is clarified that, although all these solutions coincide well in the case of stationary solutions, the first approximation of the asymptotic method has comparatively large quantitative error in the case of nonstationary solutions. In addition, the influences of the anisotropic nonlinear components which do not appear in the first approximation of the asymptotic method are investigated.

Nonstationary Oscillation of a Rotating Shaft With Nonlinear Spring Characteristics During Acceleration Through a Major Critical Speed (A Discussion by the Asymptotic Method and the Complex-FFT Method)

1997 ◽  
Vol 119 (1) ◽  
pp. 31-36 ◽  
Author(s):  
Y. Ishida ◽  
K. Yasuda ◽  
S. Murakami
Keyword(s):  
Steady State ◽  
Asymptotic Method ◽  
Critical Speed ◽  
Approximate Solutions ◽  
Rotating Shaft ◽  
Amplitude Variation ◽  
Nonlinear Spring ◽  
First Approximation ◽  
Polar Coordinate ◽  
Nonstationary Oscillations

Nonstationary oscillations during acceleration through a major critical speed of a rotating shaft with nonlinear spring characteristics are discussed. First, the first approximate solutions of steady-state and nonstationary oscillations are obtained by the asymptotic method. Second, the amplitude variation curves of each oscillation component are obtained by the complex-FFT method. It is clarified that the first approximation of the asymptotic method has comparatively large quantitative error in the case of nonstationary solutions. In addition, the influences of each nonlinear component in polar coordinate expression on nonstationary oscillations are investigated.

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